Concurrent access control is an old problem in many fields in Computer Science. It has been solved in many languages and systems, using mechanisms like monitors or priority queues. Nowadays computers implement multi-core capabilities. This means that they are virtually capable of execution of processes in parallel. This requires new techniques and open new issues in the field of concurrent access control. Moreover, most operating systems are multi-user; thus, we have to focus on a multi-processor multi-user scenario. Trust becomes a paramount aspect when building distributed applications; the same applies on a lower scale in modern computers. We propose the use of a trust graph that keeps record of the trust relationships of the system and helps in deciding on concurrent access requests. The information encoded in the graph will be used both in order to decide on the access requests and to order granted requests in terms of their associated trust level